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arXiv:2603.18078

Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification

Dibakar Sigdel

Published Mar 18, 2026• 0 citations
arXivHTMLPDF

Abstract

We present the Variational Phasor Circuit (VPC), a deterministic classical learning architecture on the continuous $S^1$ unit-circle manifold. Inspired by variational quantum circuits, VPC replaces dense weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space, giving a unified method for binary and multi-class classification of spatially distributed signals. We evaluate VPC on real motor-imagery electroencephalography (EEG) from the PhysioNet Motor Movement/Imagery database (10 subjects, Common Spatial Pattern features, subject-wise cross-validation), where it attains a mean decoding accuracy of $0.60$ -- the highest among standard brain--computer-interface baselines (linear discriminant analysis, logistic regression, RBF-SVM, and a multilayer perceptron) -- using an order of magnitude fewer parameters and the lowest cross-subject variance. We also characterize capacity honestly: with phase-only shifts and unitary mixing, VPC realizes a linear decision function in a fixed cosine/sine feature lifting, well matched to the largely separable band-power structure of EEG but unable to represent parity-type functions, a ceiling that depth does not raise. These results position unit-circle phase interference as a parameter-efficient alternative to dense neural computation for signal classification, and motivate VPC both as a standalone classifier and a front-end for hybrid phasor-quantum systems.

DOI
10.48550/arxiv.2603.18078

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Brain tumor image classification is an essential pre-processing task for tumor diagnosis and treatment planning. In medical imaging, quantum computing analyse medical imaging data, offering potential speedups and new representations compared to classical methods. The brain images are transformed through resizing and normalization to a uniform 32 × 32 × 3 resolution. Subsequently, these processed images are converted into vectors to enable encoding into quantum states. The feature set is reduced using Principal Component Analysis (PCA) to ensure compatibility with the restricted qubit count in the quantum circuits. Through amplitude encoding, these vectors are mapped to quantum states, allowing for a compact and efficient data representation within the quantum domain. A parameterized Variational Quantum Circuit(VQC), consisting of entangling gates and trainable rotations, processes the encoded quantum states to learn features that can effectively discriminate between classes. The loss is calculated from the measured expectation values of Pauli-Z observables and optimized using classical gradient descent, where the objective function is the mean squared error. The trained quantum model is designed for multi-class classification, specifically distinguishing between meningioma, glioma tumors, pituitary tumors, and the absence of a tumor. The outcome of this proposed work demonstrates the VQC’s advantage over classical baselines, including Random Forest, and Support Vector Machine (SVM) and Multi-Layer Perceptron (MLP). The VQC achieved the highest accuracy of 95% and the best robustness (Specificity 0.983). Crucially, the VQC accomplished this using only 24 trainable parameters, showcasing a significant increase in parameter efficiency compared to the classical models. The novelty of this work is the quantitative demonstration that a custom-designed, resource-efficient quantum model can outperform established classical deep learning methods in both performance and efficiency for complex medical image classification. The VQC provides a 3.5-fold gain in parameter efficiency, achieving the highest accuracy of 95% using only 24 trainable parameters. This efficiency is enabled by the novel application of amplitude encoding to the medical images, which compresses 16 features into just 4 qubits. The VQC demonstrates robustness vital for medical diagnostics, achieving a Specificity of 0.983. Its shallow architecture is also NISQ-friendly and remains stable by avoiding the Barren Plateau issue (Gradient Norm: 0.11), validating the path toward quantum advantage in diagnostic tools. The results of this approach highlight the potential amplitude encoding in quantum machine learning, as a feasible and effective method for classifying real-world medical images. This work also opens avenues for future hybrid quantum-classical diagnostic systems that could utilize richer quantum state encodings for significant gains in computational efficiency and accuracy.
Electroencephalography (EEG) provides a powerful non-invasive modality for capturing millisecond-scale brain dynamics, yet traditional analysis pipelines often rely on hand-crafted features and classical models with limited ability to capture nonlinear dependencies. This study introduces Q-EEG, a novel quantum-enhanced computational framework for brain state classification. The proposed approach integrates classical pre-processing with quantum machine learning to exploit the representational capacity of quantum circuits. Raw EEG signals are first band-pass filtered into canonical rhythms—delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz), and gamma (30–100 Hz)—and artefact removal is performed using ICA. Average band powers are then computed via the PSD and assembled into feature vectors. These normalized features are embedded in quantum states via rotation gates, forming the initial input to a VQC. The VQC models cross-frequency relationships using parameterised rotating layers and entangling operations, with weights trained using hybrid classical–quantum training with the parameter-shift rule and gradient-based optimisers. The computational basis classifies via measurements and evaluates the framework on seizure-versus-non-seizure detection tasks. Compared to SVM and Random Forest, accuracy, precision, recall, and F1-score are measured. Experimental results show that quantum-enhanced EEG analysis may capture complex brain patterns, enabling scalable, interpretable, and clinically useful diagnostic systems. This study shows that Q-EEG can bridge neuroscience with quantum computing, enabling clinical translation.
ABSTRACT Brain tumor classification from magnetic resonance imaging requires discriminating subtle morphological differences that confound both radiologists and automated pipelines. Existing quantum machine learning architectures for medical imaging provide no mechanism to preserve non‐local spatial structure during feature encoding, discarding the inter‐region phase relationships and boundary periodicity that separate tumor subtypes. A six‐qubit hybrid quantum–classical architecture, QuMo, is introduced in which Moiré beat‐field geometry is injected into the amplitude‐encoding pipeline before variational optimization. A depthwise‐separable convolutional encoder extracts spatial feature maps; the Moiré‐Modulation (MoMo) operator applies frequency‐controlled multiplicative interference to yield geometrically expressive, sparse amplitude vectors; and a variational quantum circuit trained by simultaneous perturbation stochastic approximation learns a task‐specific unitary. Over five seeded trials on the BraTS and Kaggle brain tumor benchmarks, QuMo reaches accuracy at 62 total gate layers, a depth and CNOT reduction relative to the raw‐encoding variational baseline, and records the highest accuracy and lowest cross‐trial variance among seven quantum reference architectures. Inter‐class Euclidean separation is verified independently of classifier output to increase by at least across 5432 cross‐class feature pairs. MoMo satisfies all three conditions of the Geometry‐Driven Implementation Flexibility framework, improving seven downstream classical, hybrid and quantum classifiers.
Abstract This paper presents a parallel quantum–classical hybrid architecture for image classification that integrates classical feature extraction with parallel quantum processing while maintaining competitive performance and improving parameter efficiency. Low-level and intermediate image features are first extracted by a shared convolutional neural network and then processed by multiple parallel quantum branches. Each branch employs a multilayer variational quantum circuit with a rotation–entanglement–rotation structure. To enhance representation diversity, two encoding-specific strategies are introduced. For amplitude encoding, deterministic spatial permutations generate distinct structural views of the same feature map across branches. For angle encoding, a layer-wise data re-uploading mechanism injects complementary feature subsets into different branches and circuit layers. Heterogeneous entanglement topologies with dynamic routing further diversify qubit interactions without increasing the number of trainable parameters. The measured expectation values from all branches are concatenated and fed into a compact linear classifier. Experiments on MNIST, CIFAR-10, and a thermal image dataset show that the proposed architecture achieves 98.35% accuracy on MNIST and competitive results on the other two datasets, while using substantially fewer parameters in the classification head than a fully classical baseline with the same feature extractor. These results demonstrate that parallel quantum processing combined with structured data embedding can serve as an effective and parameter-efficient decision stage for image classification.